The class \(GH^\infty \) — Since however \(G^\infty (\Omega )\)  may be too big, one can use as a variant the set \(GH^\infty (\Omega )\)  of maps where one assumes that the functions \(f_J\)  in (REF ) takes values in \(\Lambda _L\) , for \(L<L^{\prime }\) : it can be shown that, for many purposes is is enough to choose the integers \(L\)  and \(L^{\prime }\)  such that \(2k< L^{\prime }\le 2L\)  (see [1]}). The resulting theory is similar to the algebro-geometric theory of supermanifolds with flesh.
